I used to fret about such issues as well, but now I'm really quite apathetic to it. After all, what real relevance does biology have? It's a set of chemicals, a set of chromosomes, it's nothing to do with WHO you are, that's all that matters. Who you are will shine out brighter than anything else, beyond any biology. And in any case, the fact you are trans is likely to have some biological basis anyway, whether it be based in the brain structure or somewhere else.
The fact I never had a female upbringing, although painful, is something I'm actually proud of now. I like being different, it's difference and creativity that stands out and can achieve greatness. I have a different perspective on life and gender, and I'm my own kind of woman. I love to sing and my androgynous singing voice is different to many of those samey female vocals one hears nowadays.
Why be normal, blend in and live and die like the billions of other people on this planet? Why not have lived a different and interesting life, being your own self. I'm not necessarily saying to be "out and proud" about being trans - I certainly have don't go round shouting it from the rooftops, but I find as long as you have people around you who accept and love you, that's all you need. Anyway, there are other women with hysterectomies, ovary and womb problems who have to have the same treatments we do. I even know of a woman who had cervical cancer and after a surgery, she lost width in her vagina so she has to periodically dilate it.
You say you have to "catch up" with the other girls - on what exactly? Some people believe that they should 'learn' to be a woman and catch up on how to act as a female, particularly those who transition when older. Perhaps my perspective is different than others who transitioned when older but I never consciously learned to be female or attempted to 'catch up' - I just did what comes naturally, and people often comment on how feminine my persona is, which surprises me, because I'm honestly not 'trying' at all, just doing what comes naturally. The only person you have to catch up with is yourself, and being who you really are - and that's a journey many people make.